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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Semi-analytic solutions to the Noh problem with a black box EoS

The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Clinical Applications of Geometrical Field Matching in Radiotherapy Based on a New Analytical Solution

A new analytical formalism has been published recently that provides all the parameters necessary for geometrical field matching in radiotherapy. The present work applies the general expressions for craniospinal irradiation, breast irradiation with a supraclavicular half-field, and breast irradiation with a supraclavicular full-field. We also explore the formalism as a tool to analyze and compare different techniques. Field matching is achieved by imposing both parallelism and coincidence between the side planes of adjacent fields. The rotation angles and either the field aperture for a certain isocenter position or the isocenter coordinates for a given field aperture are supplied. All of the already known exact solutions are reproduced. New expressions for the field aperture and for the isocenter coordinates, which were not previously available, are also computed. If tangential fields at a fixed source-to-skin distance are used together with a supraclavicular full-field, different apertures for each tangential field are required to achieve a correct match. If an isocentric technique for the tangential fields or a supraclavicular half-field is used, this complication is avoided. The breast technique with the supraclavicular half-field is recommended, because it presents several advantages with respect to the supraclavicular full-field. This formalism provides a useful tool in cases where matching of adjacent fields is necessary.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2010

Properties of the exact analytic solution of the growth factor and its applications

There have been the approximate analytic solution [V. Silveira and I. Waga, Phys. Rev. D 50, 4890 (1994).] and several approximate analytic forms [W. J. Percival, Astron. Astrophys. 443, 819 (2005).][S. M. Carroll, W. H. Press, and E. L. Turner, Annu. Rev. Astron. Astrophys. 30, 499 (1992).][S. Basilakos, Astrophys. J. 590, 636 (2003).] of the growth factor D{sub g} for the general dark energy models with the constant values of its equation of state {omega}{sub de} after Heath found the exact integral form of the solution of D{sub g} for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both {omega}{sub de}=-1 or -(1/3)[S. Lee and K.-W. Ng, arXiv:0905.1522.] and the general dark energy models with the constant equation of state {omega}{sub de}[S. Lee and K.-W. Ng, Phys. Lett. B 688, 1 (2010).] independently. We compare the exact analytic solution of D{sub g} with the other well known approximate solutions. We also prove that the analytic solutions for {omega}{sub de}=-1 or -(1/3) in [S. Lee and K.-W. Ng, arXiv:0905.1522.] are the specific solutions of the exact solutions of the growth factor for general {omega}{sub de} models in [S. Lee and K.-W. Ng, Phys. Lett. B 688, 1 (2010).] even though they look quite different. Comparison with the numerical solution obtained from the public code is done. We also investigate the possible extensions of the exact solution of D{sub g} to the time-varying {omega}{sub de} for the comparison with observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

ExactPack: A python library of exact analytic solutions

Verification of multi-physics simulation software against problems with known analytic or semi-analytic solutions is an important aspect of research into a wide variety of fields involving the motion of fluids, shock physics and other dynamic material properties. Previous work comparing simulation results against analytic solutions has been ad-hoc, with developers frequently writing their own analytic solvers. This has resulted in a large amount of duplicated effort. The python library ExactPack has been developed as a collection of analytic and semi-analytic solvers to a variety of multi-physics problems, providing a consistent API to a set of well-tested solver implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstroem space-time: Analytical solutions

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstroem space-time in terms of the Weierstrass weierp, {sigma}, and {zeta} elliptic functions. Based on the study of the polynomials in the {theta} and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstroem space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstroem space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations

In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Development of an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs

In this study, we have developed an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs where fluid flow through the fracture is radial. The dimensionless forms of the governing equations and the initial and boundary conditions in the radial flow system can be written in a form identical to those in the linear flow system developed by Jung and Pruess [Jung, Y., and K. Pruess (2012), A Closed-Form Analytical Solution for Thermal Single-Well Injection-Withdrawal Tests, Water Resour. Res., 48, W03504, doi:10.1029/2011WR010979], and therefore the analytical solutions developed in Jung and Pruess (2012) can be applied to compute the time dependence of temperature recovery at the injection/withdrawal well in a horizontally oriented fracture with radial flow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2010

Analytical solution for Joule-Thomson cooling during CO2 geo-sequestration in depleted oil and gas reservoirs

Mathematical tools are needed to screen out sites where Joule-Thomson cooling is a prohibitive factor for CO{sub 2} geo-sequestration and to design approaches to mitigate the effect. In this paper, a simple analytical solution is developed by invoking steady-state flow and constant thermophysical properties. The analytical solution allows fast evaluation of spatiotemporal temperature fields, resulting from constant-rate CO{sub 2} injection. The applicability of the analytical solution is demonstrated by comparison with non-isothermal simulation results from the reservoir simulator TOUGH2. Analysis confirms that for an injection rate of 3 kg s{sup -1} (0.1 MT yr{sup -1}) into moderately warm (>40 C) and permeable formations (>10{sup -14} m{sup 2} (10 mD)), JTC is unlikely to be a problem for initial reservoir pressures as low as 2 MPa (290 psi).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Push-pull tests for estimating effective porosity: expanded analytical solution and in situ application

The analytical solution describing the one-dimensional displacement of the center of mass of a tracer during an injection, drift, and extraction test (push-pull test) was expanded to account for displacement during the injection phase. The solution was expanded to improve the in situ estimation of effective porosity. The truncated equation assumed displacement during the injection phase was negligible, which may theoretically lead to an underestimation of the true value of effective porosity. To experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted across six test wells located in a shallow, unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injection of bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6–5.0%) were substantially greater than from the truncated equation (0.1–1.3%). The expanded and truncated equations were compared to data from previous push-pull studies in the literature and demonstrated that displacement during the injection phase may or may not be negligible, depending on the aquifer properties and the push-pull test parameters. The results presented here also demonstrated the spatial variability of effective porosity within a relatively small study site can be substantial, and the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (< ± 0.5%). The tests presented here are also the first that the authors are aware of that estimate, in situ, the effective porosity of fine-grained fill material.

58 GEOSCIENCES↗
DOE OSTI2013

ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS

Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

A new analytic solution for 2nd-order Fermi acceleration

A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Analytical solution and parameter estimation for heat of wetting and vapor adsorption during spontaneous imbibition in tuff

An analytical expression is derived for the thermal response observed during spontaneous imbibition of water into a dry core of zeolitic tuff. Sample tortuosity, thermal conductivity, and thermal source strength are estimated from fitting an analytical solution to temperature observations during a single laboratory test. Here, the closed-form analytical solution is derived using Green's functions for heat conduction in the limit of “slow” water movement; that is, when advection of thermal energy with the wetting front is negligible. The solution has four free fitting parameters and is efficient for parameter estimation. Laboratory imbibition data used to constrain the model include a time series of the mass of water imbibed, visual location of the wetting front through time, and temperature time series at six locations. The thermal front reached the end of the core hours before the visible wetting front. Thus, the predominant form of heating during imbibition in this zeolitic tuff is due to vapor adsorption in dry zeolitic rock ahead of the wetting front. The separation of the wetting front and thermal front in this zeolitic tuff is significant, compared to wetting front behavior of most materials reported in the literature. This work is the first interpretation of a thermal imbibition response to estimate transport (tortuosity) and thermal properties (including thermal conductivity) from a single laboratory test.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0 . In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0 . The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

42 ENGINEERING↗
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
DOE OSTI2020

Hybrid Analytics Solution for Power Plant Operations

Expert Microsystems, Inc., MapEx Software Inc. and XMPLR Energy LLC have teamed to submit a proposal to the US Department of Energy’s Office of Fossil Energy to improve the efficiency, reliability and flexibility of existing coal-based power plants. The project, titled Hybrid Analytics Solution to Improve Coal Power Plant Operations (the “Hybrid Analytics” project), will develop, demonstrate and commercialize a novel approach that integrates two proven real-time monitoring techniques. The Hybrid Analytics approach integrates into a single, integrated solution: a) an established, advanced data-driven analytics solution that includes artificial intelligence, advanced pattern recognition and machine-learning techniques and b) a well-proven, first principle thermal heat balance model solution. The future role of coal plants will depend on the ability to cycle and follow loads to meet marginal power demands, accommodate renewables and support the grid. Essential to success in this new role is a plant’s ability to maintain high reliability, efficiency and flexibility. However, these changing operational demands put significant stresses on power plant components that directly impact the ability to deliver these requirements. In the past, plants have independently monitored performance using physics-based solutions (heat rate, boiler losses, etc.) and reliability using data-driven analytics (advanced pattern recognition). The Hybrid Analytics solution integrates both approaches to enhance fault detection, provide automated diagnostics and estimates of remaining time to act, and provide critical, enhanced and accurate real-time information to coal plant operators. As a result, coal plants can improve efficiency, reliability, and flexibility and can cost-effectively maintain their key role in the power delivery system.

01 COAL, LIGNITE, AND PEAT↗